First slide

Average Speed

Question

A vehicle travels half the distance l with speed v₁ and the other half with speed v₂, then its average speed is [NCERT Exemplar]

Moderate

A

$\frac{v_{1} + v_{2}}{2}$
B

$\frac{2 v_{1} + v_{2}}{v_{1} + v_{2}}$
C

$\frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$
D

$\frac{l (v_{1} + v_{2})}{v_{1} v_{2}}$

Solution

Time taken to travel first half distance, $t_{1} = \frac{l / 2}{v_{1}} = \frac{l}{2 v_{1}}$
Time taken to travel second half distance, $t_{2} = \frac{l}{2 v_{2}}$
Total tIme $= t_{1} + 1 t_{2} = \frac{l}{2 v_{1}} + \frac{l}{2 v_{2}} = \frac{l}{2} (\frac{1}{v_{1}} + \frac{1}{v_{2}})$
We know that, v_av = Average speed
$= \frac{total distance}{total time} = \frac{l}{\frac{l}{2} (\frac{1}{v_{1}} + \frac{1}{v_{2}})} = \frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$

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